Kastoryano, Michael J.Lucia, Angelo2024-01-172024-01-172018Kastoryano M J and Lucia A 2018 Divide and conquer method for proving gaps of frustration free Hamiltonians J. Stat. Mech. 2018 0331051742-546810.1088/1742-5468/aaa793https://hdl.handle.net/20.500.14352/93629Providing system-size independent lower bounds on the spectral gap of local Hamiltonian is in general a hard problem. For the case of finite-range, frustration free Hamiltonians on a spin lattice of arbitrary dimension, we show that a property of the ground state space is sufficient to obtain such a bound. We furthermore show that such a condition is necessary and equivalent to a constant spectral gap.engjournal articlehttps://doi.org/10.1088/1742-5468/aaa793restricted accessQuantum phase transitionsRigorous results in statistical mechanicsSpin chainsLadders and planesFísica (Física)22 Física